Is the Dewar whose name is on the famous whiskey related to scientist Sir John Dewar, who created the vacuum bottle?

The Scottish physicist and chemist Sir James Dewar (1842-1923) invented the thermal insolation device that made it possible to keep gases liquified in 1906. The vacuum flask is the everyday version of Dewar's device.
I'll leave it to someone else to make the connection with the whiskey, now I've put you right on the name.

There's no indication of a link in the biographical information for Sir James Dewar:

https://en.wikipedia.org/wiki/James_Dewar

Information about the origins of the company (John Dewar & Sons) who originally made the whisky is harder to come by, but that company was evidently founded in Perth whereas Sir James' family were innkeepers in Kincardine, near Stirling. Whilst it isn't impossible that there is a link, the two families seem not to be closely related. Dewar is not an especially uncommon name.